Duplicate detection of 2D-NMR Spectra

2D-Nuclear magnetic resonance (NMR) spectra are used in the (structural) analysis of small molecules. In contrast to 1D-NMR spectra, 2D-NMR spectra correlate the chemical shifts of 1H and 13C at the same time. A spectrum consists of several peaks in a two--dimensional space. The most important information of a peak is the location of its center, which captures the bonding relationships of hydrogen and carbon atoms. A spectrum contains much information about the chemical structure of a product, but in most cases the structure cannot be read off in a simple and straightforward manner. Structure elucidation involves a considerable amount (manual) efforts. Using high-field NMR spectrometers, many 2D-NMR spectra can be recorded in short time. So the common situation is that a lab or company has a repository of 2D-NMR spectra, partially annotated with the structural information. For the remaining spectra the structure in unknown. In case two research labs are collaborating, the repositories will be merged and annotations shared. We reduce that problem to the task of finding duplicates in a given set of 2D-NMR spectra. Therefore, we propose a simple but robust definition of 2D-NMR duplicates, which allows for small measurement errors. We give a quadratic algorithm for the problem, which can be implemented in SQL. Further, we analyze a more abstract class of heuristics, which are based on selecting particular peaks. Such a heuristic works as a filter step on the pairs of possible duplicates and allows false positives. We compare all methods with respect to their run time. Finally we discuss the effectiveness of the duplicate definition on real data.